A Mean Value Theorem for the Diophantine Equation $axy-x-y=n$

preprint2011arXivOpen access

In this paper, we prove an asymptotic formula for the average number of solutions to the Diophantine equation $axy-x-y=n$ in which $a$ is fixed and and $n$ varies.

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A Mean Value Theorem for the Diophantine Equation $axy-x-y=n$

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A Mean Value Theorem for the Diophantine Equation axy−x−y=naxy-x-y=naxy−x−y=n

Abstract

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A Mean Value Theorem for the Diophantine Equation $axy-x-y=n$